Not related to rhymes, but I remember at school, we used to have massive skipping games with about 30 girls, and "boundaries" - when it got to your turn, you ran in, jumped, ran out, and then had to run round the boundaries and join the queue again. If you missed your jump, you had to turn the rope. To make it more difficult, we sometimes jumped in "against" the rope, that's with the rope turning away from you, so you had to avoid tripping over it on the way out.

We must have been extremely fit compared with kids these days!

Just remembered another rhyme:

My mammy told me
If I was good - ee
That she would buy me
A rubber dolly

My auntie told her
I kissed a soldier
Now she won't buy me
A rubber dolly

You did "doublers" at the end of each line, I think.

When we were out playing it was "My mother told me, if I was goody, she would buy me a rubber johnny"

This was one you said if you were just using your skipping rope by yourself - skipping fast not jumping:
Charlie Chaplin went to France
To teach the ladies how to dance
And this is how he taught them
Heel toe lairey oh
Quick march under the arch
Roundabout turn! ( Jump at that point)

Vote,vote,vote for (insert full name of skipper)
Call in (insert 1st name of new skipper) from the door
For (name of new skipper) is a lady and she's going to have a baby
So we don't need (1st skipper) anymore.

Bumper car, Bumper car number 49,
Whizzing round the corrrrrnnnner (you have to run round one of the turners on the end and jump back in)
Please put on your brakes Sir (stop jumping with one leg either side of the rope)

Bumper car, Bumper car number 49,
Whizzing round the corrrrrnnnner (you have to run round one of the turners on the end and jump back in)
Please put on your brakes Sir (stop jumping with one leg either side of the rope)